In a medium bowl, combine the drained tuna, mayonnaise, dijon mustard, celery, red onion, lemon juice, and garlic powder. Mix well with a fork, breaking up any large chunks of tuna. Season with salt and black pepper to taste.
Spread a thin layer of softened butter on one side of each slice of sourdough bread.
Place the bread slices butter side down. Divide the tuna mixture evenly and pile it onto the 4 bread slices. Top each open-faced sandwich with a slice of sharp cheddar cheese.
Preheat the air fryer to 360°F for 2 minutes.
Carefully place the open-faced tuna melts in the air fryer basket. Air fry for 5 to 7 minutes until the bread is golden and toasted on the bottom and the cheese is melted and bubbly on top.
Remove the tuna melts from the air fryer and let them cool for 1 minute before serving. These are perfect on their own or paired with a cup of soup.